http://www.theteachersguide.com/lesson%20plans/Math/MEA0001.html


Evaluation of Area and Volume Lesson


Piaget's and Vygotsky's research suggests that cognitive development occurs in students as they collaborate together. Although their theories differ on whether biology or social interaction comes first in development, both agree that collaboration and modeling among students are important to development, as they allow for students to help one another, and this allows for students to see different perspectives. Similarly, the same active, collaborative learning that these men would recommend for the cognitive developmental process would also be recommended by those who support the information processing theory of learning as well. This theory suggests that by being actively engaged with material, as the students in this lesson plan will be, the brain is able to store and retrieve information more effectively. This plan also emphasizes the importance of giving students no initial instruction, and therefore having them construct the knowledge on their own. This notion coincides with the idea of constructivist learning, the final aspect of learning and development that appears in his plan. Containing all three important aspects of development, this lesson plan on area and volume was designed very consistently with developmental research.

Piaget believed that students between the ages of seven and eleven, the age range of the third grade students the lesson plan was designed for falling into that category, were in a "concrete operational" stage. In this stage, he believed students were not quite able to understand abstract ideas, and thus relied on concrete example to understand their world. The creator of this lesson plan appears to concur with that notion when he explains that some math concepts are "too abstract," and "too hard to grasp," and therefore need to be replaced with a "concrete model" that students can actually see. Thus, the students create their own concrete, three dimensional models of geometric objects in a text book. Then when students are trying to accomplish the objectives of the lesson, that is, describing the difference between area and volume, and understanding how various units of measure relate to one another, they can use the picture in their head of this model to help them understand. Thus, this three dimensional model is a very helpful learning aid for students at this age.

However, having students collaborate to create three dimensional models also demonstrates the teacher's understanding of another aspect of cognitive development. When students use teamwork to solve problems, when they cooperate to build models, they are actively learning through social interaction. Both Piaget and Vygotsky believed that interaction was an important experience for development. They felt that using peer models would be helpful to development as well, and therefore recommended asking students to help one another, for this allows not only for all students to better understand the material, but also for them to see each other's differing perspectives.

Although it is not explicitly mentioned, it can be assumed that the group work designed in the lesson plan was also allowing for modeling, as Piaget and Vygotsky recommended. It seems reasonable that the students would be expected help one another, since they were placed into groups and given very limited directions. Furthermore, after the group projects are complete, a spokesperson for each group explains to the rest of the class what their group chose to create and why. By being forced to explain the project, those students presenting are obliged to learn as much as possible about the project, since asking a student to explain something is a very productive way of ensuring even they understand it better. Thus, by using peer modeling, not only is the entire class able to learn more from the models of each presentation, and able to better understand other groups' approaches to the same challenge, but each presenter also learns more from their own project as they explain it to the others.

Yet the group activity that supports the ideas of cognitive development also coincides with the theory of information processing. According to this theory, students must focus on material in order to increase the chances of it being transferred to short term memory, stored, transferred to long term memory, and then later retrieved. For this to occur, students need to be "interested" and "stimulated" in the lesson, as this plan suggests. By being actively engaged, by collaborating, students pay more attention to the material and therefore greatly increase their chances of remembering information later.

Yet besides causing students to be more interested, and therefore more focused on the lesson, the group work coincides with ideas of information processing in other ways as well. The three dimensional models they construct serve as visual aids, and allow them to form associations in their minds to help them recall the visual images later when trying to picture geometric objects in order to solve problems with them. Associating visual images with ideas is very helpful in learning, because the brian was created to deal with a visual world, and it thus stores and recalls visual information easily. Thus, the elaborative rehearsal that occurs when the concrete models of geometric shapes become associated images in the mind is concurrent with the ideas of information processing as well, and it will, as the teacher hoped, leave a 'lasting memory' for his students.

Constructivism is the final aspect of development that the teacher demonstrated a good understanding of in this lesson plan. By emphasizing the importance of providing students with only the materials, but no initial instruction, this plan causes students to discover for themselves how geometric shapes are created, and thus, understand how area and volume are calculated. This social constructivism causes students to take the little information provided in the introduction to the lesson, and create new schemas, or modify old ones, to account for the new information they gather as they work together in groups. Thus, they must be able to apply the little information they learn, as well as the knowledge they gain through experimenting together, and use this to construct a meaning out of the lesson, in this case, to construct concepts of area and volume.

Furthermore, by realizing these concepts for themselves, the students will be able to relate the concepts of area and volume that they discover to other shapes and other problems. By learning on their own, the students will be able to develop general rules for the concepts of area and volume, and apply them to many situations, as opposed to being taught a rule by a teacher, and needing the concepts or area and volume in each individual situation to then be taught as well. Thus, through their discoveries, the students develop an understanding of the relationship between shapes, their area, and their volume, and then can transfer this idea and apply it to other situations, in order to figure out different problems without needing to remember each separate formula for every existing shape.

In addition, by discovering the relationship for themselves, students will then be able to best understand the meaning, and best make associations that will help them retain and retrieve the information for a much longer period of time than they would if they were simply given the formulas by the teacher. By discovering for themselves, their brains will understand the entire discovery process, and thus having many meanings and make many associations that will help storage and retrieval. Thus, since they were more focused and more engaged with the material during constructivist learning, they will be able to retain and recall the information longer, just as the information processing theory suggests as well.

This lesson plan involves ideas that are consistent with many different aspects of learning and development. Collaboration and modeling are present, as Piaget and Vygotsky recommend for cognitive development. The use of visual images to help store and retrieve information in this lesson concur with the suggestions of the information procession theory. Finally, the student-initiated discovering during the lesson coincides with the idea of constructivist learning as well. SInce it correctly adheres to all of these theories, this lesson plan is very consistent with research on learning and development.